Online Local Volatility Calibration by Convex Regularization
Online Local Volatility Calibration by Convex Regularization
复制标题
通过凸正则化进行在线局部波动率校准
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Zubelli
中科院分区：
文献类型：
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作者：
V. Albani;J. Zubelli
本文研究了由市场给定的期权价格标定局部波动率曲面的逆问题。我们将不断增加的期权价格信息流整合到Dupire的局部波动率模型中。这导致在适当的函数空间中，随着时间的推移，考虑局部波动率表面及其相应的价格，这些价格由观察到的基础股票价格指数化。数据映射的结果参数在适当的Bochner-Sobolev空间中定义。在这个框架下，我们证明了关键的正则性。这使我们能够建立一个校准技术，结合在线方法与凸吉洪诺夫正则化工具。这种方法被用来解决局部波动率识别的反问题。其结果是，我们证明了收敛速度相对于噪声和相应的离散为基础的正则化参数的选择。最后，我们通过数值试验来说明理论结果。
We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing flow of option price information into the well-accepted local volatility model of Dupire. This leads to considering both the local volatility surfaces and their corresponding prices as indexed by the observed underlying stock price as time goes by in appropriate function spaces. The resulting parameter to data map is defined in appropriate Bochner-Sobolev spaces. Under this framework, we prove key regularity properties. This enable us to build a calibration technique that combines online methods with convex Tikhonov regularization tools. Such procedure is used to solve the inverse problem of local volatility identification. As a result, we prove convergence rates with respect to noise and a corresponding discrepancy-based choice for the regularization parameter. We conclude by illustrating the theoretical results by means of numerical tests.
Banach 空间中 Tikhonov 正则化的序贯差异原理的正则化性质
影响因子：
1.1
作者：
S. W. Anzengruber;B. Hofmann;P. Mathé
通讯作者：
P. Mathé